The Beale / Howson emails in full at The Starcourse

This is the original un-edited set of Beale/Howson letters. Two factual amendments are made by {note }  

Fri, 20 Mar 1998 17:52:23

Dear Colin  
I'm not saying there are no other conceivable explanations: we both know that there are always conceivable alternatives given any set of observations. But lets apply the normal canons of philosophical and scientific evaluation.  
Most theists believe in a Loving Ultimate Creator, most rational atheists believe in Quantum Uncaused Stuff, tracing matter/energy/everything to the Big Bang (or more speculatively to a Quantum Seed) but no further. Let's call these views Red and Green respectively, and use accepted standards for testing hypotheses:  
  • simplicity of statement; 
  • explanatory power and 
  • likelihood of observed facts. 
As to simplicity of statement: almost everyone has concepts of love and of creating, but the quantum world-view depends on abstruse mathematics, the basic interpretation of which is far from agreed. Of course simply stated views are often wrong, but between two hypotheses of equal power that equally fit the facts we should prefer the simpler.  
Since Red offers explanations of why Quantum Stuff should exist at all, of why the universe should be comprehensible and of an objective basis to morality, so has greater explanatory power than Green.  
Testing against 'observed facts' is more difficult: anything involving love is intensely personal. But I think there are five areas where we can reach some agreement on the evidence and likelihoods, although with our different prior probabilities we may still reach different conclusions.  
The first is that scientists now appreciate that the universe appears to be very finely 'tuned' to produce life. For example, if the balance between expansion and contraction of the Universe, or the ratio of the mass of the electron and proton were minutely different from their present values, it seems that intelligent life could not exist. Crude estimates of the likelihood that a random universe could support life give values less than 1 in 10^20 and although various somewhat speculative schemes increase this there is no evidence that under Green the odds against life are less than a million to one. Attempts to explain this away by suggesting that "there may be millions of other universes" don't wash such a device could 'explain' any unlikely observation. Nor does the retort that "if it were not so we would not be here to observe it" this is true of many other facts (that we have brains, for example) but does not render the evidence inadmissible. Under Red the likelihood of a Universe that supports intelligent life is 1, under Green it is less than one in a million.  
The second area is the extraordinary accuracy of mathematical predictions and the strange fact that our perceptions of mathematical beauty turn out to be a reliable guide to physics. Dirac {note acually it was Einstein} remarked, "The most {note actually 'one'} incomprehensible thing about the universe is that it is comprehensible". Green explains why we might evolve the mathematics needed to hunt and avoid predators, but offers no explanation of why this sort of mathematics can predict the movements of binary pulsars to accuracies of better than 1 in 10^20.  
Is torturing babies for fun always wrong, or is this just a matter of opinion? Only a complete moral relativist, who holds that eg torturing babies for fun could be OK, can deny that there are some objective moral truths. Most versions of Green accept the existence of objective morality, explaining this by adding some additional basic moral axioms. Under Red this is grounded on the reality of God's love, under Green it is another unexplained 'brute fact'.  
Fourthly, there is the Phenomenon of Jesus. Most believers in Red find his life, teaching, death and resurrection utterly compelling. Believers in Green generally agree that he was a great moral teacher, and accept that something must have happened around the first Easter to give the disciples the utter conviction that they had seen, touched and spoken with their risen Master.  
The disciples didn't fake the resurrection  no-one would die for something they knew to be a lie. The authorities could not produce Jesus' body  that would have killed Christianity at birth. So, under Green, what are the alternatives?  
1.If Jesus did die, we have an unknown grave-robber, who then did not earn an enormous reward from the authorities by producing the body, and large-scale mass hallucination. Not impossible, but there is no reason to put the likelihood of this careless robber higher than 1%, and such strong mass hallucinations are very rare indeed.  
2.So maybe Jesus survived, and then deliberately deceived the disciples into believing in the resurrection? The odds against surviving crucifixion must have been at least 1,000:1 and would a great moral teacher lie to his friends in a way that would clearly cause their deaths? Green implies that one of these, or something like them, must have happened.  
Freak coincidences do occur, but again we have an observation whose likelihood under Green is less than one in a million.  
So here are four sets of observations, two more readily quantifiable than the others, whose combined likelihood is more than one million million times higher under Red than under Green. This does not mean that belief in Green is irrational, but seems to me that it does show that the arguments for Red are 'almost overwhelming'.  

Mon, 23 Mar 1998 14:17:49

Dear Nicholas,  
I hold no brief for the view that there is only 'quantum stuff'. I am agnostic; I don't think the available evidence justifies any inference to statements of ultimate causation - or lack of it. Let's proceed from there.  
You invoke 'accepted standards for testing hypotheses'. These, you claim, are simplicity, explanatory power and likelihood (the probability of the data given the hypothesis). I disagree, and so would many scientists, especially of the Bayesian tendency (an elementary account of this is given in a book by Peter Urbach and me, Scientific Reasoning: the Bayesian Approach, Open Court, second edition 1993). The base-rate fallacy shows that likelihoods by themselves have no evidential value: they are informative only in conjunction with prior probabilities. We can always fix up some absolutely incredible hypothesis that describes in exact detail what we have observed, but that of course tells us nothing. Simplicity is hard to pin down, and it's hardly an accepted standard: many people (including me) are simplicity-sceptics.  
Now to your more specific claims. You claim that 'Red' can explain  
(i) why 'quantum stuff should exist at all';  
(ii) the apparent comprehensibility of the universe; and  
(iii) objective moral standards.  
I can't allow (iii): that there's an objective morality is a hypothesis, not a fact, and one which the vast majority of moral philsophers reject. So (iii) begs the question. That leaves (i) and (ii).  
I am amazed that you can say that 'Red' explains (i). 'Red' has nothing to say at all about the physical structure of this universe. Indeed, it is the complete emptiness of 'Red' on detail that explains why people have largely switched their interest to scientific accounts of the universe rather than religious ones.  
So we proceed to (ii). You say that 'Red' explains why the universe is comprehensible to us, whereas science doesn't. We seem to be good at constructing very accurate mathematical theories in a way, you claim, that ordinary evolutionary pressures can't explain. Your claim that the neurological development required for advanced mathematics is unlinked to the sorts of cognitive abilities favouring survival in primitive environments is implausible. It is known that mathematics can be entirely developed within a conceptual system consisting only of general logic and the relation 'x is a member of [collection, or set] y'. So a general classificatory ability, which surely was adaptive, will, surprisingly, suffice to discuss Hilbert spaces, affine connections, gauge fields etc.  
Now the second question: why, if 'Red' were false, the universe should be so accommodating as to reveal its structure. This begs the question again, just like your (iii). It has not been established that the physical universe is comprehensible to us. Indeed, there is little evidence (pace Hawking) that it will turn out to be. The predictive successes of quantum theory and Relativity don't imply the truth of those theories and might well be accidental. Indeed, give that the theories seem to be inconsistent with each other that is not unlikely.  
Now let's look at your other claims on behalf of 'Red'.  
(a) You say that under 'Red' the probability of a universe that supports intelligent life is 
1; otherwise it is highly improbable, given the degree of fine tuning of the physical constants required for the universe to support life. I think you are assuming some unwarranted things about probability; that aside, these values do not support 'Red'. 
We're back to the uninformativeness of bare likelihoods again. Toss a fair coin enough times and you'll get a result as improbable as that or more, but you wouldn't claim that it was evidence that the coin is unfair.  
(b) You claim that if I deny - I do - that there are objective moral truths then I must accept that torturing babies for fun is OK. Not true. I have ideals of conduct that I find compelling, and I believe that a society which accepted them would be preferable to one that didn't. Ideals and preferences are neither true nor false, but they can certainly be compelling. Moreover, as philosophers from Hume and Kant onwards have rightly pointed out, there is no moral value merely in obeying the wishes and commands of someone else, whether they love you or not.  
(c) You claim that the secular alternatives to the Christian account of the resurrection of Jesus give the gospel reports very low probability. Firstly, I repeat my warning about likelihoods in isolation. Secondly, it's not clear that these probabilities are very substantial given 'Red', since 'Red' says nothing about those events. Thirdly, there are other more plausible explanations; e.g. Jesus did not die on the cross, but was taken down before death, later revived, helped to escape, and shortly afterwards selectively reappeared. In view of its propaganda value the resurrection myth was encouraged. One such account is given by Barbara Thiering, a theologian and biblical scholar, in her book Jesus the Man (Corgi, 1992). You can't object that this explanation contradicts the gospels and so has low likelihood, since it's illegitimate to assume the gospels to be literally true. Apart from the fact that they contradict each other, that would beg the question again. If they were any ordinary ancient text, of course, it would be conceded that they would have to be expertly deciphered. In spite of that much (particularly in St John) is consistent with this account.  
One fact you don't mention is the horrifying ubiquity of innocent suffering. In the light of this the probability of 'Red' should surely be zero.  

Thu, 26 Mar 1998 14:39:22

Dear Colin  
Your book puts forward an interesting case that all you need is Bayes' Theorem (considering only likelihoods with prior probabilities, and disregarding the other criteria) but you concede that this is still a minority view, citing Einstein and many others against you. Some of the key points on both sides seem almost impossible to address with your exclusively Bayesian approach. For example, how can we estimate the likelihood of the presently observed level of suffering under either Red or Green? Or that the Universe obeys mathematical laws under Green? But since, as I have indicated, Red is preferable to Green on each of the normal criteria, even disregarding one or two tends to the same conclusion.  
Let's consider two people, Mr R and Mr G, who are virtually certain of Red and Green respectively, but who are willing to consider, at least for the purposes of discussion, a tiny probability (say 0.1%) that the other could be right [Note to Prof. Howson: if we use tiny to mean c. 0.1% and virtually certain to mean c. 99.9% we can remain mathematically rigorous without putting people off]. Someone who gives a zero prior probability to an opposing view (a Bigot) will dismiss any evidence however compelling, and can never have a rational discussion about it. Suppose, for example, that Miss Rose is trapped in an airless room with a combination lock and can only escape with the right 6 digit combination. She has a number-generating Gizmo, which Green says is purely random (so the likelihood of producing the combination is 1 in a million) and Red says is designed so that she will live (so the likelihood is 1). She gets the right combination. It might just be a million-to-one chance. But applying your Baysean methods, if Mr G began virtually certain that the Gizmo was random he should end virtually certain that it was designed. A Green Bigot will still believe Green, in the teeth of any odds or evidence, and might posit millions of other Miss Roses just to evade the conclusion.  
Even if Red really did say nothing about the physical structure of the universe it at least offers an explanation of why the universe exists at all. This has long been known, but the remarkable fine-tuning of the fundamental constants of the universe has not (see The Anthropic Cosmological Principle by Barrow & Tippler or Quarks, Chaos & Christianity by John Polkinghorne FRS, who estimates the odds involved as one in a trillion, so my suggestion of one in a million is generous to Green).  
The maths issue is not "why can our brains do our mathematics?" (although it has been shown that maths, complete with realised infinities, isn't quite as simple as you suggest) but "why can our mathematics predict the universe?" To escape this you are driven to suggest that "the predictive success of Quantum Mechanics and General Relativity Ëmight be accidental." Both of these have given remarkable predictions (about hyperfine emission spectra and the movements of binary pulsars) which have been verified to better than 1 part in 10^20. Some accident!  
And although I don't accuse you of saying "torturing babies for fun is OK", you are asserting that this is a matter of opinion (whereas "there is no moral value in merely obeying commands" is a fact?) It seems we can choose between belief in God or belief in possibly-subjectively-OK baby-torture and accidental physics.  
You ask why Red implies the Resurrection? The Incarnation (the ultimate loving communication) has at least high probability given Red, and clearly, given the Incarnation, the Resurrection is virtually certain. Of course there are possible Green explanations (including time-travelling Fundamentalists from the 24th Century) but the problem is not "conflict with the Bible" but positing occurrences which we know on other grounds are improbable. There must have been over 100,000 crucifixions, but no known instances of un-reprieved crucified people surviving. Perhaps a few did, and kept quiet, but still the proportion must be tiny. There have been many great moral teachers, is there any evidence that any of them lied to their friends in a way that foreseeably caused their friends deaths? Again, the proportion must be tiny. This Green 'explanation' is about as likely as the Random Gizmo.  
You suggest that Red is refuted by the observed level of innocent suffering. But, as your book explains, this requires you to show that, if Red were true, the probability of the currently observed level of innocent suffering would be exactly zero. Even if we accept that a loving ultimate creator would not allow serious human suffering without sufficient reasons, can you demonstrate that an ultimate creator could not possibly have such reasons? I'm sure I don't fully understand them, but I can see what some of them might be:  
if the purpose of the universe is to bring into being persons who are free to love, then there must be freedom for persons to inflict suffering on others and to alleviate their suffering; suffering seems to be an essential part of learning to love; and suffering not caused by persons is caused by the processes that drive the physics and biology which are a vital part of our coming into being.  
It's not clear how to estimate the likelihood, under either Red or Green, of the suffering we observe. It sometimes looks rather low. Christians do not forget the cry "my God, my God, why have your forsaken me?" But we also see a God that takes suffering onto Himself and transforms it into hope through resurrection. Under the Christian flavour of Red, suffering at least makes some kind of sense: under Green it is another meaningless fact. But even if the likelihood were as low as 1 in a million under Red, and as high as 10% under Green, then applying the Baysean calculations you advocate, it only partially cancels out either the first argument (Anthropic Universe) or the fourth (Jesus).  
So what are we left with? Red is simpler to state, and has greater explanatory power. It gives substantially higher likelihoods on two of the roughly quantifiable observations but lower on one other. Following the methods advocated in your book, Mr G still ends up virtually certain of Red. In addition, to escape two other arguments you have to suggest that the accuracy of General Relativity and Quantum Mechanics is accidental and that whether "torturing babies for fun is OK" is a matter of opinion.  

Fri, 27 Mar 1998 09:44:19

Dear Nicholas,  
I repeat what I said in my first letter, that I hold no brief for 'Green'. With that in mind, let's proceed to 'fine-tuning'. In the joint range of the possible values of certain constants, you find that only a very small interval of them is compatible with life. What does that tell you about the likelihood of a creator? Nothing by itself. You have to look at how likely you think the alternative possibilities are. In your lift example there's another hypothesis, that Miss Rose without divine intervention knows something about the right combination, which to my mind would seem vastly more probable than the divine hypothesis, whose prior probability would be effectively zero. In the case of the physical constants I would consider the wider alternative to Red, that it happened that way for other reasons presently unknown. Since I would indeed assign zero probability to Red because I think it's refuted (see below), the 'other reasons unknown' hypothesis gets my vote; that's why I'm an agnostic.  
I don't think Einstein was anti-Bayesian; I don't believe he ever considered the matter explicitly. It is true that he didn't accept that God played dice with the world; neither did another great physicist, and even greater mathematician, the arch-determinist and co-founder-member of Bayesianism, Laplace. He memorably said that Bayesianism was commonsense reduced to a calculus.  
I certainly didn't suggest that mathematics was simple (I never found it so). I said that the only conceptual apparatus, apart from logic, that you need for mathematics is simple. That doesn't stop mathematics being difficult, any more than knowing the chess pieces stops chess being difficult. Completed infinities, incidentally, are stipulated to exist by axioms formulated within that simple language.  
Now to successful predictions. No physicist I've spoken believes that quantum mechanics in anything like its present form will emerge as the True theory - if there is one. If they are right then its predictions, however precise, will turn out to have been accidental, arising from a false theory. The very distinguished mathematician and physicist Poincare said a century ago that the predictions of Newtonian theory, a theory now rejected, were so accurate that they couldn't have been accidental. Ironically, he was also the first to point out that any finite set of data, however precise, can in principle be accounted for in infinitely many distinct ways: in other words, as a matter of logical fact there have simply got to be quite a lot (at least as many as the cardinal number of the set of real numbers, aptly called 'uncountable') of 'accidents'.  
The resurrection story, or stories, is widely regarded as one of the weakest points in the Christian canon. According to the synoptic gospel on which the other two are thought to be based (Mark), Pilate 'marvelled' that it took Christ only six hours to die: it frequently took days to die on the cross. The relevant reference class for survival probabilities is not that of all people crucified, as you suggest, but that of healthy young males taken down after a very short time, in circumstances where it is no easy matter to determine the point of death and indeed where, according to another account, there were still signs of life. Moreover, the authentic part of Mark ends merely with the discovery two days after the crucification that Jesus had vanished (16; 8); an event hardly surprising if Christ was revived and helped to escape (as the young man present suggested). The rest of the gospel was added by other hands, and in ways contradicted elsewhere. On any informed probability distribution over the various possibilities in the light of what we know about the genesis of the gospels and their historical context, the probability of any of the resurrection stories being true should be zero. Not almost zero, zero.  
Finally, the suffering problem. In answer to your question, yes, if we mean the same things by the words we utter, I would have thought it self-evident that a loving creator, not acting under compulsion, would not, in your words, make 'freedom for persons to inflict suffering on others'. You yourself say that it's objectively wrong to torture babies for fun. So probability zero again. I don't know about Green, but on the evidence Red should go.  

Fri, 27 Mar 1998 14:53:04

Dear Colin  
Now when science goes against your arguments you resort to "other reasons presently unknown". The truth of Newtonian predictions is far from "accidental" they are the limiting case of the deeper, more complex, theories of GR & QM, which are actually more consonant with a Christian world-view. Laplace took determinism too far he was so sceptical that he pronounced comets mythical.  
So when the scientific and philosophical arguments have all gone against you, you turn to selective interpretation of the Bible. Look at the short time, ignore the previous torture and exhaustion and the spear thrust from a Roman soldier (who, if he had let Jesus live, would have been crucified himself). The definitive medical account of Jesus' death, published in the Journal of the American Medical Association deals with this nonsense. Nor do dubious speculations about the origins of the Bible help your case. Unless you can produce a single instance of an un-reprieved crucified man not dying, you must concede the that probability is tiny, just as I concede that it is not zero. Nor have you addressed the tiny probability, even if he had survived, of a great moral teacher lying to his disciples in this way. You simply repeat that you have a closed mind, all evidence and arguments for Red are to be disregarded, the probability is "zero, zero".  
Because, you claim, whatever the strength of the other arguments, Red is refuted, incontrovertibly logically disproved, by the fact that there is "freedom for persons to inflict suffering on others" (and that they do so). This would only be true if "Loving" means "always preventing suffering". Would a mother who painlessly killed her otherwise healthy children, on the grounds that this would always prevent their suffering, be loving? At any rate, this is not what Red means by love, and you can't expect to refute Red without understanding it.  
Take away your purported refutation, based on a misunderstanding, and what are you now left with? "Reasons presently unknown" and selective interpretation of the Bible (to bolster a theory with a tiny tiny likelihood) and accidental physics and subjectively-OK-baby-torture.  

Sat, 28 Mar 1998 19:38:37

Dear Nicholas,  
I am not 'resorting to' agnosticism. I made it absolutely clear in every one of my letters to you (your memory can't be that short) that that was my position. I stressed this so much because I feared, justifiably as it turns out, that you would try to misrepresent me as an advocate of your 'Green' - a position for which I think there is no positive evidence either.  
Newtonian theory, according to its successors, is wrong on just about every fundamental: it is not Lorentz-invariant, its spacetime is flat, it is not a quantum theory. Any false theory has some true consequences; those of a fundamentally false theory will be accidentally true. That they're explained by a later theory is neither here nor there.  
As for 'selective interpretation of the Bible': what alternative is there? - it's inconsistent. So it can't all be true. I'm certain that the resurrection is one bit that isn't (Jesus casting devils into a herd of pigs is one of many others). The few uncontroversial facts are consistent with entirely unmiraculous explanations, some far from implausible. One is that Jesus was taken down before death, revived, and helped escape. Your counterargument is to cite a 'definitive medical account' of his death, and claim that 'a great moral teacher' wouldn't connive at a deception. Do you really think that a 'definitive medical account' can be based on the pot-pourri of mutually inconsistent anecdotes collected, copied and embellished by the authors of the gospels, who had an axe to grind? And Jesus a great moral teacher? How many great moral teachers tell people who reject their teaching that their fate will be worse than that of the inhabitants of Sodom and Gomorrah on the Day of Judgment, or would say 'But those, mine enemies, which would not that I should reign over them, bring them hither, and slay them before me'? {note: Prof Howson now accepts that this last is a quote from a Despot in a parable and thus it is deleted from the Prospect article}- hardly a person to jib at deceiving for the greater good (even if he did; who knows what actually happened?). And everyone, in principle, has to give zero prior probability to some logical possibilities. I personally think the resurrection a particularly deserving case.  
I have no idea what 'love' means in the mouth of someone who claims to love someone they're torturing. It must mean something I don't understand, you say. I said earlier that I assumed we were speaking the same language. If we are, Red is false. 
Return to the Discussion 
Ref 1. Edwards, et al. "On the Physical Death of Jesus Christ." Journal of American Medical Association. Vol 255 21 March 1986: 1455. Extracts from this article are on the web here.